Certificate for #2791 ⟨a, b | aaaaaaabbba=1⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with a < b < c < d
• Auxiliary generators:
  1. aaaaaaaa=c
  2. bbb=d

Axiom: aaaaaaabbba=1.

Referenced by [4].

Axiom: aaaaaaaa=c.

Defines rule #8.

Referenced by [6], [7], [12], [13].

Axiom: bbb=d.

Defines rule #7.

Referenced by [4], [5].

Overlap of [1] aaaaaaabbba=1 with [3] bbb=d:

Critical pair: aaaaaaada=1.

Referenced by [7], [8], [9], [11].

Overlap of [3] bbb=d with [3] bbb=d:

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #5.

Referenced by [10].

Overlap of [2] aaaaaaaa=c with [2] aaaaaaaa=c:

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.

Overlap of [2] aaaaaaaa=c with [4] aaaaaaada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [9].

Overlap of [4] aaaaaaada=1 with [4] aaaaaaada=1:

Critical pair: aaaaaaad=aaaaaada.

Flip LHS and RHS.

Referenced by [11].

Overlap of [7] cda=a with [4] aaaaaaada=1:

Critical pair: cd=aaaaaaada.

Reduce RHS:

Defines rule #3.

Referenced by [10], [12], [13].

Overlap of [9] cd=1 with [5] db=bd:

Critical pair: cbd=b.

Referenced by [14].

Overlap of [8] aaaaaada=aaaaaaad with [8] aaaaaada=aaaaaaad:

Critical pair: aaaaaadaaaaaaad=aaaaaaadaaaaada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [12], [13].

Overlap of [11] aaaada=aaaaad with [11] aaaada=aaaaad:

Critical pair: aaaadaaaaad=aaaaadaaada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [13].

Overlap of [12] da=ad with [2] aaaaaaaa=c:

Critical pair: dc=adaaaaaaa.

Reduce RHS:

Defines rule #6.

Referenced by [14].

Overlap of [10] cbd=b with [13] dc=1:

Critical pair: cb=bc.

Defines rule #2.